Can you make a bump map using grey scale after you texture paint?
It is possible to directly paint your bump maps and view it real time. 

Its a little hard to see in the GIF but works perfect close up. 



Here is a flat plane (Not subdived). 



This is the render view 



Just make a new image texture and make sure it is set to 50% grey, So when you paint white it bumps up and black bumps down. 




This is what the image texture looked like after painting.